Observations of $_12CO$ J = 1 – 0 and HCN J = 1 – 0 emission from NGC 5194 (M51) made with the 50 m Large Millimeter Telescope and the SEQUOIA focal plane array are presented. Using the HCN-to-CO ratio, we examine the dense gas mass fraction over a range of environmental conditions within the galaxy. Within the disk, the dense gas mass fraction varies along the spiral arms but the average value over all spiral arms is comparable to the mean value of interarm regions. We suggest that the near-constant dense gas mass fraction throughout the disk arises from a population of density-stratified, self-gravitating molecular clouds and the required density threshold to detect each spectral line. The measured dense gas fraction significantly increases in the central bulge in response to the effective pressure, $P_e$, from the weight of the stellar and gas components. This pressure modifies the dynamical state of the molecular cloud population and, possibly, the HCN-emitting regions in the central bulge from selfgravitating to diffuse configurations in which $P_e$ is greater than the gravitational energy density of individual clouds. Diffuse molecular clouds comprise a significant fraction of the molecular gas mass in the central bulge, which may account for the measured sublinear relationships between the surface densities of the star formation rate and molecular and dense gas.